It is well known that apparent resistivity (Ra) is quite different from the true formation resistivity (Rt) in complex formation environments. Efforts have been made to apply inversion techniques to derive Rt from Ra. The advantages of using inversion are that the method automatically derives a Rt model and that the inverted model is consistent with the logs. Inversion improves bed boundary definition and the water saturation calculation. However, there are two bottlenecks to the method, i.e. the processing speed and solution uniqueness. Because of these problems, inversion still has not been routinely used in log interpretation.rnThe major part of the processing time in a rigorous inversion algorithm is spent on calculating the Jacobian matrix that sets the direction of model adjustment. In this 1-D fast algorithm, the Jacobian matrix calculation is avoided. The fast algorithm first applies a shaping filter to the logs. Equivalently, on a first order approximation, the shaping filter maximizes the diagonal elements of the Jacobian matrix as well as symmetrizes the Jacobian matrix. The shaping filter differs from the conventional focusing filters in that it has no resolution enhancement. It only ensures that for each log point of the reshaped log the largest sensitivity is from the formation at the same depth point. The inversion solution is then updated iteratively according to the difference between the filtered log and the calculated tool response (with the same shaping filter applied) of the predicted model.rnThe stability of the inverse algorithm is achieved by using the fact that induction measurements have little sensitivity to a resistive layer with thickness smaller than the main coil spacing. A simple automatic adjustment in correction step length is built into the algorithm to avoid resistivity over-correction and consequently the instability in updating the model. The algorithm converges to a stable Rt model typically after three to five iteration steps. Since there is no Jacobian matrix calculation, the total computation time is roughly equal to the cost of a single forward run multiplied by the number of iterations.
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